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Absorption imaging is a commonly adopted method to acquire, with hightemporal resolution, spatial information on a partially transparent object. Itrelies on the interference between a probe beam and the coherent response ofthe object. In the low saturation regime, it is well described by a BeerLambert attenuation. In this paper we theoretically derive the absorption of a$\sigma$ polarized laser probe by an ensemble of two-level systems in anysaturation regime. We experimentally demonstrate that the absorption crosssection in dense $^{87}$Rb cold atom ensembles is reduced, with respect to thesingle particle response, by a factor proportional to the optical density b ofthe medium. To explain this reduction, we developed a model that incorporates,in the single particle response, the incoherent electromagnetic backgroundemitted by the surrounding ensemble. We show that it qualitatively reproducesthe experimental results. Our calibration factor that has a universaldependence on optical density $b$ for $\sigma$ polarized light : $\alpha$ =1.17(9) + 0.255(2)b allows to obtain quantitative and absolute, in situ, imagesof dense quantum systems.

Quantitative absorption imaging of optically dense effective two-level systems